Anatoly Yakovlevich Dorogovtsev (September 7, 1935–April 22, 2004)

Translated by:
V. Zaiats

Journal:
Theor. Probability and Math. Statist. **71** (2005), 191-199

DOI:
https://doi.org/10.1090/S0094-9000-06-00658-2

Published electronically:
January 4, 2006

Full-text PDF Free Access

References |
Additional Information

References
- A. Ja. Dorogovcev,
*Statistical analysis of a difference stochastic equation*, Selected Transl. Math. Statist. and Prob., Vol. 3, Amer. Math. Soc., Providence, R.I., 1962, pp. 315–319. MR **0154364**
- A. Ja. Dorogovcev,
*Confidence intervals associated with the evaluation of parameters*, Selected Transl. Math. Statist. and Prob., Vol. 3, Amer. Math. Soc., Providence, R.I., 1962, pp. 321–325. MR **0154363**
- A. Ja. Dorogovcev,
*Remarks on random processes generated by certain differential equations*, Dopovidi Akad. Nauk Ukraïn. RSR **1962** (1962), 850–853 (Ukrainian, with Russian and English summaries). MR **0143250**
- A. Ja. Dorogovcev,
*Some remarks on the extrapolation of processes generated by differential equations*, Dopovidi Akad. Nauk Ukraïn. RSR **1962** (1962), 1006–1010 (Ukrainian, with Russian and English summaries). MR **0143005**
- A. Ja. Dorogovcev,
*Some remarks on differential equations perturbed by periodic random processes*, Ukrain. Mat. Ž. **14** (1962), 119–128 (Russian, with English summary). MR **0141850**
- A. Ja. Dorogovcev,
*Correlation functions of vector processes satisfying a certain differential equation*, Ukrain. Mat. Ž. **14** (1962), 322–325 (Russian). MR **0155351**
- A. Ya. Dorogovtsev,
*Statistical Problems for a Class of Non-Stationary Random Processes*, Candidate dissertation, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1962. (Russian)
- A. Ya. Dorogovtsev,
*Some remarks on the processes generated by some differential processes*, Vestnik Kiev University, Ser. Mat. Mekh. **5** (1963), 124–146. (Russian)
- A. Ja. Dorogovcev,
*Problems of linear extrapolation for a class of vector processes*, Ukrain. Mat. Ž. **16** (1964), 830–834 (Russian). MR **0172330**
- I. I. Gihman and A. Ja. Dorogovcev,
*On the stability of solutions of stochastic differential equations.*, Ukrain. Mat. Ž. **17** (1965), no. 6, 3–21 (Russian). MR **0281278**
- A. Ja. Dorogovcev,
*Certain problems of optimal control of a regression experiment*, Dopovīdī Akad. Nauk Ukraïn. RSR Ser. A **1968** (1968), 1067–1072 (Ukrainian, with Russian and English summaries). MR **0247659**
- A. Ja. Dorogovcev,
*An application of dynamic programming methods to the study of a certain problem of technical servicing*, Teor. Verojatnost. i Mat. Statist. **1970** (1970), no. vyp. 1, 74–85 (Russian). MR **0280176**
- A. Ja. Dorogovcev,
*The design of a regression experiment*, Teor. Verojatnost. i Mat. Statist. Vyp. **3** (1970), 56–61 (Russian, with English summary). MR **0283928**
- A. Ja. Dorogovcev,
*A certain non-parametric estimator of the regression function*, Teor. Verojatnost. i Mat. Statist. Vyp. **4** (1971), 61–64 (Russian, with English summary). MR **0288918**
- V. V. Breĭ, A. Ja. Dorogovcev, O. A. Makoveckiĭ, and L. V. Pogorelyĭ,
*The optimal choice of a rarefaction interval*, Teor. Verojatnost. i Mat. Statist. **7** (1972), 14–22, 162 (Russian, with English summary). MR **0343356**
- V. V. Breĭ, L. V. Pogorelyĭ, and A. Ja. Dorogovcev,
*Determination of the characteristics of a certain nonstationary process*, Vyčisl. Prikl. Mat. (Kiev) **19** (1973), 137–142, 160 (Russian, with English summary). MR **0341584**
- A. Ja. Dorogovcev and Ju. V. Kartašev,
*The estimation of the mean value of a stationary process when there is a given time of observation. I*, Teor. Verojatnost. i Mat. Statist. **Vyp. 8** (1973), 50–58, 175 (Russian, with English summary). MR **0426335**
- A. Ja. Dorogovcev,
*The estimation of an almost periodic signal from observation in a stationary noise*, Questions of statistics and of the control of random processes (Russian), Izdanie Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev, 1973, pp. 74–105 (Russian). MR **0433767**
- A. Ja. Dorogovcev,
*Remarks on the properties of a certain least squares estimator*, Dopovīdī Akad. Nauk Ukraïn. RSR Ser. A (1973), 585–590, 667 (Ukrainian, with English and Russian summaries). MR **0331679**
- A. Ya. Dorogovtsev and K. P. Makarenko,
*On least squares estimates of parameters of a certain nonlinear system*, Issled. Operatsiĭ ASU **2** (1973), 42–52. (Russian)
- A. Ja. Dorogovcev and Ju. V. Kartašev,
*The estimation of the mean value of a stationary process in the case of given duration of observation time. II*, Teor. Verojatnost. i Mat. Statist. **Vyp. 9** (1973), 73–81, 175 (Russian, with English summary). MR **0426336**
- A. Ja. Dorogovcev,
*The existence and convergence of the moments of the least square estimator in a nonlinear autoregression model*, Dopovīdī Akad. Nauk Ukraïn. RSR Ser. A (1973), 1066–1071, 1149 (Ukrainian, with English and Russian summaries). MR **0331680**
- A. Ja. Dorogovcev,
*Estimation of the probability of small values of sums of positive random variables*, Teor. Verojatnost. i Mat. Statist. **Vyp. 9** (1973), 66–72, 175 (Russian, with English summary). MR **0413231**
- A. Ja. Dorogovcev,
*The asymptotic properties of least square estimators for regression coefficients*, Problemy Peredači Informacii **9** (1973), no. 4, 49–57 (Russian). MR **0348949**
- A. Ya. Dorogovtsev and Yu. V. Kartashev,
*On an estimate of the mean value of a stationary process for a given size of a sample*, Theory Probab. Appl. **XVIII** (1973), no. 4, 871. (Russian)
- A. Ja. Dorogovcev,
*The estimation of an almost periodic signal from observation in a stationary noise*, Questions of statistics and of the control of random processes (Russian), Izdanie Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev, 1973, pp. 74–105 (Russian). MR **0433767**
- A. Ja. Dorogovcev,
*Consistency of a certain estimate of the parameter of a stochastic differential equation*, Teor. Verojatnost. i Mat. Statist. **Vyp. 10** (1974), 72–81, 175 (Russian, with English summary). MR **0428646**
- A. Ja. Dorogovcev and Ju. V. Kartašev,
*Least square estimations of the regression coefficient of a random process with prescribed observation time*, Teor. Verojatnost. i Mat. Statist. **Vyp. 10** (1974), 82–87, 175 (Russian, with English summary). MR **0423717**
- A. Ja. Dorogovcev,
*Asymptotic properties of estimators of the parameters of a signal that is amplitude modulated by a random process*, Dopovīdī Akad. Nauk Ukraïn. RSR Ser. A (1974), 680–684, 763 (Ukrainian, with English and Russian summaries). MR **0348950**
- A. Ja. Dorogovcev,
*The estimation of the mean value of a stationary process in the case of restricted possibilities of observation*, Dokl. Akad. Nauk SSSR **214** (1974), 261–263 (Russian). MR **0341784**
- A. Ya. Dorogovtsev,
*Asymptotic properties of least squares estimates for a non-linear autoregressive model*, Teoriya Sluchainyh Processov **2** (1974), 47–54. (Russian)
- A. Ja. Dorogovcev,
*Consistent estimation of a discrete signal on the basis of observation with random errors*, Teor. Verojatnost. i Mat. Statist. **11** (1974), 26–34, 178 (Russian, with English summary). MR **0394996**
- A. Ja. Dorogovcev,
*A certain property of the estimate of an almost periodic signal*, Teor. Verojatnost. i Mat. Statist. **Vyp. 11** (1974), 35–38, 178 (Russian, with English summary). MR **0405757**
- A. Ja. Dorogovcev,
*The asymptotic behavior of estimates of the parameters of a certain nonlinear system*, Kibernetika (Kiev) **4** (1974), 72–77 (Russian, with English summary). MR **394995**
- A. Ja. Dorogovcev,
*On an estimate of a periodic signal on the basis of observations with stationary noise*, Vīsnik Kiïv. Unīv. Ser. Mat. Meh. **16** (1974), 10–25, 172 (Ukrainian, with English and Russian summaries). MR **0455240**
- A. Ja. Dorogovcev,
*The consistency of a certain estimate of the regression function*, Teor. Verojatnost. i Mat. Statist. **Vyp. 12** (1975), 36–44, 171 (Russian, with English summary). MR **0397973**
- A. Ja. Dorogovcev,
*Properties of parameter estimators in a certain linear regression model*, Vīsnik Kiïv. Unīv. Ser. Mat. Meh. **17** (1975), 3–12, 176 (Ukrainian, with English and Russian summaries). MR **0433768**
- A. Ja. Dorogovcev and T. A. Šermet′eva,
*The consistency of an estimate of a transition function*, Theory of random processes, Questions of statistics and control (Russian), Izdanie Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev., 1974, pp. 30–39 (Russian). MR **0488576**
- A. Ja. Dorogovcev,
*On the limit distribution of an estimate for a regression function*, Teor. Verojatnost. i Mat. Statist. **Vyp. 13** (1975), 38–46, 161 (Russian, with English summary). MR **0418326**
- G. P. Grečka and A. Ja. Dorogovcev,
*The asymptotic properties of the periodogram estimate of the frequency and amplitude of a harmonic oscillation*, Vyčisl. Prikl. Mat. (Kiev) **Vyp. 28** (1976), 18–31, 150 (Russian, with English summary). MR **0451587**
- A. Ja. Dorogovcev,
*On an assertion that is useful in proving the consistency of estimators*, Teor. Verojatnost. i Mat. Statist. **Vyp. 14** (1976), 34–41, 154 (Russian, with English summary). MR **0415835**
- A. Ja. Dorogovcev,
*On the consistency of nonparametric estimators of a regression function*, Teor. Verojatnost. i Mat. Statist. **Vyp. 15** (1976), 47–53, 154. MR **0418327**
- A. Ja. Dorogovcev,
*Remarks on the properties of a certain nonparametric maximum likelihood estimate*, Mathematics collection (Russian), Izdat. “Naukova Dumka”, Kiev, 1976, pp. 262–268 (Russian). MR **0468076**
- A. Ja. Dorogovcev,
*Properties of the nonparametric estimator of the translation coefficient of the simplest stochastic differential equation*, Theory of random processes, No. 4 (Russian), Izdat. “Naukova Dumka”, Kiev, 1976, pp. 51–59, 117 (Russian). MR **0423665**
- A. Ja. Dorogovcev and P. S. Knopov,
*On the properties of an estimator for the parameters of a nonstationary Gaussian regression of a random field*, Teor. Verojatnost. i Mat. Statist. **Vyp. 15** (1976), 54–67, 155 (Russian, with English summary). MR **0431564**
- G. P. Grečka and A. Ja. Dorogovcev,
*The properties of periodogram estimation of frequency*, Vīsnik Kiïv. Unīv. Ser. Mat. Meh. **18** (1976), 120–122, 145 (Ukrainian, with English and Russian summaries). MR **0494764**
- A. Ja. Dorogovcev and P. S. Knopov,
*The consistency of estimates of a function continuous in a domain that are based on observations at a finite set of points of its range of values with random errors*, Dokl. Akad. Nauk Ukrain. SSR Ser. A **12** (1976), 1065–1069, 1140 (Russian, with English summary). MR **0433681**
- A. Ja. Dorogovcev and P. S. Knopov,
*An estimate of a two-dimensional signal from observations with additive random noise*, Teor. Verojatnost. i Mat. Statist. **Vyp. 17** (1977), 61–79, 164 (Russian, with English summary). MR **0468077**
- A. Ja. Dorogovcev and P. S. Knopov,
*Asymptotic properties of a nonparametric estimate of a function of two variables*, Theory of random processes, No. 5 (Russian), Izdat. “Naukova Dumka”, Kiev, 1977, pp. 27–35, 112 (Russian). MR **0468016**
- A. Ja. Dorogovcev,
*Properties of estimates of parameters of linear Gaussian regression in the discrete case*, Vyčisl. Prikl. Mat. (Kiev) **Vyp. 31** (1977), 136–147, 159 (Russian, with English summary). MR **0501671**
- A. Ja. Dorogovcev,
*On the convergence of the extremum-points of convergent sequences of random functionals*, Dokl. Akad. Nauk Ukrain. SSR Ser. A **7** (1977), 581–584, 669 (Russian, with English summary). MR **0494627**
- A. Ya. Dorogovtsev,
*Studies in the Theory of Estimation of Parameters of Random Processes*, Doctoral dissertation, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1977. (Russian)
- A. Ja. Dorogovcev and M. I. Judickiĭ,
*Models with random errors in variables. Estimation of parameters and design of experiments*, Teor. Verojatnost. i Mat. Statist. **19** (1978), 51–57, 157 (Russian, with English summary). MR **0518967**
- A. Ja. Dorogovcev and P. S. Knopov,
*The weak convergence of a sequence of two-parameter martingales*, Dokl. Akad. Nauk Ukrain. SSR Ser. A **8** (1978), 675–679, 767 (Russian, with English summary). MR **510436**
- A. Ya. Dorogovtsev, D. S. Silvestrov, A. V. Skorokhod, and M. I. Yadrenko,
*Probability theory: collection of problems*, Translations of Mathematical Monographs, vol. 163, American Mathematical Society, Providence, RI, 1997. Translated from the 1976 Ukrainian original by O. I. Klesov and V. A. Kotov. MR **1444579**
- A. Ya. Dorogovtsev,
*On a problem of determining an unbiased linear estimator with minimal variance*, Teor. Veroyatnost. i Mat. Statist. **22** (1980), 52–57; English transl. in Theory Probab. Math. Statist. **22** (1981), 57–62.
- N. A. Germanov and A. Ja. Dorogovcev,
*Estimation of the parameters of an autoregressive process with nonidentically distributed disturbances*, Dokl. Akad. Nauk Ukrain. SSR Ser. A **7** (1980), 14–16, 96 (Russian, with English summary). MR **582843**
- A. Ja. Dorogovcev and A. A. Kurčenko,
*Application of a problem of minimization in a Hilbert space to a determination of the best linear estimations*, Teor. Veroyatnost. i Mat. Statist. **23** (1980), 47–51, 148 (Russian, with English summary). MR **614575**
- A. Ya. Dorogovtsev and A. A. Kurčenko,
*The best linear estimate of trend parameters in the presence of errors of white noise type*, Teor. Veroyatnost. i Mat. Statist. **24** (1981), 27–34, 151 (Russian, with English summary). MR **628425**
- A. Ya. Dorogovtsev, A. A. Kurčenko, and A. G. Kukush,
*A new case for the existence of linear unbiased estimates*, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk **3** (1981), 23–29, 97 (Russian). MR **628914**
- A. Ya. Dorogovtsev,
*Teoriya otsenok parametrov sluchaĭ nykh protsessov*, “Vishcha Shkola”, Kiev, 1982 (Russian). MR **668517**
- A. Ya. Dorogovtsev,
*Stability of bounded and stationary solutions of equations with an operator coefficient subject to perturbations*, Mathematics today ’97, No. 11 (Russian), Nauchn. Izdat. “TViMS”, Kiev, 1997, pp. 43–52 (Russian). MR **1632323**
- A. Ya. Dorogovtsev,
*Estimation of the mean value parameter in a Hilbert space*, Theory of random processes, No. 11, “Naukova Dumka”, Kiev, 1983, pp. 28–31 (Russian). MR **711232**
- A. Ya. Dorogovtsev and Yu. G. Kondrat′ev,
*Some problems of infinite-dimensional analysis and their application*, Vīsnik Kiïv. Unīv. Ser. Mat. Mekh. **25** (1983), 55–70 (Ukrainian, with Russian summary). MR **746765**
- A. Ya. Dorogovtsev and A. G. Kukush,
*Optimal choice of the observation mode in a problem of estimation of the mean*, Teor. Veroyatnost. i Mat. Statist. **30** (1984), 38–45, 150 (Russian). MR **800828**
- A. Ya. Dorogovtsev,
*Convergence of certain integrals with respect to a Gaussian measure in a Hilbert space*, Dokl. Akad. Nauk Ukrain. SSR Ser. A **5** (1985), 7–8 (Russian, with English summary). MR **796167**
- A. Ya. Dorogovtsev, S. D. Īvasishen, and A. G. Kukush,
*Asymptotic behavior of solutions of the heat equation with white noise in the right-hand side*, Ukrain. Mat. Zh. **37** (1985), no. 1, 13–20, 133 (Russian). MR **780908**
- A. Ya. Dorogovtsev,
*The asymptotic behavior of solutions of the Cauchy problem for an abstract stochastic differential equation*, Uspekhi Mat. Nauk **41** (1986), no. 4, 159–160. (Russian)
- A. Ya. Dorogovtsev, N. Zerek, and A. G. Kukush,
*Asymptotic properties of estimates of nonlinear regression in Hilbert space*, Teor. Veroyatnost. i Mat. Statist. **35** (1986), 36–43, 122 (Russian). MR **885663**
- A. Ya. Dorogovtsev,
*Mathematical Analysis*, A collection of problems, “Vyshcha Shkola”, Kiev, 1987. (Russian)
- A. Ya. Dorogovtsev, N. Zerek, and A. G. Kukush,
*Weak convergence to the normal distribution of an estimator for an infinite-dimensional parameter*, Teor. Veroyatnost. i Mat. Statist. **37** (1987), 39–46, 135 (Russian). MR **913908**
- N. A. Denis′evskiĭ and A. Ya. Dorogovtsev,
*On the law of large numbers for a linear process in a Banach space*, Dokl. Akad. Nauk SSSR **295** (1987), no. 2, 276–279 (Russian); English transl., Soviet Math. Dokl. **36** (1988), no. 1, 47–50. MR **902681**
- A. Ya. Dorogovtsev,
*The existence of periodic solutions of an abstract stochastic equation. The asymptotic periodicity of solutions of the Cauchy problem*, Uspekhi Mat. Nauk **42** (1987), no. 4, 160. (Russian)
- A. Ya. Dorogovtsev, S. D. Īvasishen, and A. G. Kukush,
*On the asymptotic behaviour of the linear stochastic heat equation solutions*, Probability theory and mathematical statistics, Vol. I (Vilnius, 1985) VNU Sci. Press, Utrecht, 1987, pp. 419–431. MR **901501**
- A. Ya. Dorogovtsev and A. G. Kukush,
*Asymptotic behavior of the solution of the Cauchy problem for a stochastic equation of parabolic type*, Ukrain. Mat. Zh. **40** (1988), no. 2, 162–169, 270 (Russian); English transl., Ukrainian Math. J. **40** (1988), no. 2, 136–142. MR **941500**, DOI https://doi.org/10.1007/BF01056468
- A. Ya. Dorogovtsev and A. G. Kukush,
*On the limiting distribution of extremum points for certain stochastic optimization models*, Stochastic optimization (Kiev, 1984) Lect. Notes Control Inf. Sci., vol. 81, Springer, Berlin, 1986, pp. 17–21. MR **890965**, DOI https://doi.org/10.1007/BFb0007078
- A. Ya. Dorogovtsev,
*Asymptotic behavior of the solutions of the Cauchy problem for an abstract stochastic differential equation*, Teor. Veroyatnost. i Mat. Statist. **38** (1988), 31–34, 134 (Russian); English transl., Theory Probab. Math. Statist. **38** (1989), 31–34. MR **947518**
- A. Ya. Dorogovtsev,
*Existence of periodic solutions of an abstractly stochastic equation. Asymptotic periodicity of the solutions of the Cauchy problem*, Teor. Veroyatnost. i Mat. Statist. **39** (1988), 47–52, 126 (Russian); English transl., Theory Probab. Math. Statist. **39** (1989), 55–60. MR **947930**, DOI https://doi.org/10.1090/s0094-9000-2013-00873-4
- A. Ya. Dorogovtsev and Le Vin′Tkhuan,
*The existence of periodic and stationary regimes of discrete dynamical systems in a Banach space*, Kibernetika (Kiev) **6** (1988), 121–123, 136 (Russian, with English summary). MR **986181**
- J. Neyman,
*On a statistical problem arising in routine analyses and in sampling inspections of mass production*, Ann. Math. Statistics **12** (1941), 46–76. MR **4452**, DOI https://doi.org/10.1214/aoms/1177731785
- A. Ya. Dorogovtsev and Le Vin’Tkhuan,
*Correlation functions of Gaussian Markov stationary and periodic processes in a Hilbert space*, Selected Problems in the Current Theory of Random Processes, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1988, pp. 61–65. (Russian)
- M. F. Gorodniĭ and A. Ya. Dorogovtsev,
*Stationary solutions of a two-dimensional stochastic difference equation in a Banach space*, Stochastic analysis and its applications (Russian), Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1989, pp. 25–33, ii (Russian). MR **1064769**
- A. Ya. Dorogovtsev,
*Èlementy obshcheĭ teorii mery i integrala*, “Vyshcha Shkola”, Kiev, 1989 (Russian). MR **995843**
- A. Ya. Dorogovtsev,
*Periodic solutions of evolution differential equations that are perturbed by stochastic processes*, Ukrain. Mat. Zh. **41** (1989), no. 12, 1642–1648, 1727 (Russian); English transl., Ukrainian Math. J. **41** (1989), no. 12, 1412–1419 (1990). MR **1042961**, DOI https://doi.org/10.1007/BF01056109
- A. Ya. Dorogovtsev,
*Necessary and sufficient conditions for existence of stationary and periodic solutions of a stochastic difference equation in Hilbert space*, Comput. Math. Appl. **19** (1990), no. 1, 31–37. MR **1026779**, DOI https://doi.org/10.1016/0898-1221%2890%2990079-Y
- A. Ya. Dorogovtsev,
*Stationary and periodic solutions of a stochastic difference equation in a Banach space*, Teor. Veroyatnost. i Mat. Statist. **42** (1990), 35–42 (Russian); English transl., Theory Probab. Math. Statist. **42** (1991), 39–46. MR **1069311**
- A. Ya. Dorogovtsev,
*Stochastically periodic solutions of differential equations with operator coefficients*, Ukrain. Mat. Zh. **43** (1991), no. 4, 489–496 (Russian, with Ukrainian summary); English transl., Ukrainian Math. J. **43** (1991), no. 4, 451–457. MR **1117890**
- A. Ya. Dorogovtsev,
*Consistency of the least squares estimator of an infinite-dimensional parameter*, Sibirsk. Mat. Zh. **33** (1992), no. 4, 65–69, 221 (Russian, with Russian summary); English transl., Siberian Math. J. **33** (1992), no. 4, 603–607 (1993). MR **1185436**, DOI https://doi.org/10.1007/BF00971125
- A. Ya. Dorogovtsev,
*Periodicheskie i statsionarnye rezhimy beskonechnomernykh determinirovannykh i stokhasticheskikh dinamicheskikh sistem*, “Vishcha Shkola”, Kiev, 1992 (Russian, with Russian and Ukrainian summaries). MR **1206004**
- A. Ya. Dorogovtsev,
*Bounded and periodic solutions of some difference and differential equations*, Uspekhi Mat. Nauk **46** (1991), no. 6, 149–150. (Russian)
- A. Ya. Dorogovtsev,
*Mathematical Analysis*, vol. I, “Lybid”, Kyiv, 1993; vol. II, 1994. (Russian)
- A. Ya. Dorogovtsev,
*On asymptotic normality of the least square estimators of an infinite-dimensional parameter*, Ukrainian Math. J. **45** (1993), no. 1, 48–58. MR **1426569**
- A. Ya. Dorogovtsev,
*Periodic and bounded solutions of the Riccati operator equation*, Ukraïn. Mat. Zh. **45** (1993), no. 2, 239–242 (Russian, with Russian and Ukrainian summaries); English transl., Ukrainian Math. J. **45** (1993), no. 2, 255–259. MR **1232407**, DOI https://doi.org/10.1007/BF01060981
- A. Ya. Dorogovtsev,
*Stationary and periodic solutions of the Riccati operator equation with random perturbation*, Ukraïn. Mat. Zh. **45** (1993), no. 5, 609–615 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. **45** (1993), no. 5, 662–670 (1994). MR **1247681**, DOI https://doi.org/10.1007/BF01058204
- A. Ya. Dorogovtsev and M. F. Gorodniĭ,
*Bounded solutions of the operator Volterra chain*, Uspekhi Mat. Nauk **49** (1994), no. 4, 85.
- A. Ya. Dorogovtsev,
*Stationary and periodic solutions of linear differential operator equations*, Proceedings of the Second Ukrainian–Hungarian Conference on “New Trends in Probability Theory and Mathematical Statistics”, September 25–October 2, 1992, Mukachevo, Ukraine, TViMS, Kiev, 1994, pp. 50–54.
- A. Ya. Dorogovtsev and T. A. Petrova,
*Bound and periodic solutions of the Riccati equation in Banach space*, J. Appl. Math. Stochastic Anal. **8** (1995), no. 2, 195–200. MR **1330123**, DOI https://doi.org/10.1155/S1048953395000189
- M. F. Gorodniĭ and A. Ya. Dorogovtsev,
*Bounded solutions of a class of nonlinear operator difference equations*, Ukraïn. Mat. Zh. **47** (1995), no. 7, 890–896 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. **47** (1995), no. 7, 1022–1029 (1996). MR **1367944**, DOI https://doi.org/10.1007/BF01084898
- A. Ya. Dorogovtsev,
*Stability of periodic solutions of operator equations with perturbation coefficients*, Exploring stochastic laws, VSP, Utrecht, 1995, pp. 111–119. MR **1713997**
- A. Ya. Dorogovtsev,
*Stationary and periodic solutions of a certain class of nonlinear equations in a Banach space*, Theory Stoch. Process. **1(17)** (1995), no. 1, 17–25.
- A. Ya. Dorogovtsev and T. A. Petrova,
*Bounded and periodic solutions of a Riccati-type equation in a Banach space*, Dopov. Nats. Akad. Nauk Ukraïni **9** (1995), 8–9 (Russian, with English summary). MR **1374671**
- A. Ya. Dorogovtsev and T. A. Petrova,
*Bounded and periodic solutions of the operator Riccati equation with an unbounded operator*, Dopov. Nats. Akad. Nauk Ukraïni **10** (1995), 7–9 (Russian, with English summary). MR **1376464**
- A. Ya. Dorogovtsev,
*On the stability of bounded and stationary solutions of equations with operator coefficients in the case where the coefficients are disturbed*, Uspekhi Mat. Nauk **50** (1995), no. 4, 103. (Russian)
- A. Ya. Dorogovtsev,
*Asymptotic properties of an estimator of the compensator of a nonhomogeneous Poisson process*, Proceedings of the International Mathematical Conference dedicated to the memory of Hans Hahn, October 1994, Chernivtsi, “Ruta”, Chernivtsi, 1995, pp. 72–77. (Russian)
- A. Ya. Dorogovtsev and A. G. Kukush,
*Asymptotic properties of a nonparametric estimator of the intensity of a nonhomogeneous Poisson process*, Kibernet. Sistem. Anal. **1** (1996), 91–104, 188 (Russian, with English and Ukrainian summaries); English transl., Cybernet. Systems Anal. **32** (1996), no. 1, 74–85. MR **1409534**, DOI https://doi.org/10.1007/BF02366585
- A. Ya. Dorogovtsev,
*Stability of bounded and stationary solutions of linear equations with respect to perturbations of operator coefficients*, Dokl. Akad. Nauk **345** (1995), no. 4, 448–450 (Russian). MR **1376444**
- A. Ya. Dorogovtsev and T. A. Petrova,
*Bounded and periodic solutions of the Riccati operator equation with an unbounded operator*, Differ. Uravn. **33** (1997), no. 3, 309–315, 428 (Russian, with Russian summary); English transl., Differential Equations **33** (1997), no. 3, 305–311. MR **1615401**
- A. Ya. Dorogovtsev,
*Stability of stationary and periodic solutions equations in Banach space*, J. Appl. Math. Stochastic Anal. **10** (1997), no. 3, 249–255. MR **1468119**, DOI https://doi.org/10.1155/S1048953397000312
- A. Ya. Dorogovtsev,
*Stationary solutions of semilinear abstract equation with random input*, Nonlinear Stud. **5** (1998), no. 2, 129–138. MR **1652614**
- A. Ya. Dorogovtsev,
*Solutions, periodic in distribution, of the boundary value problem for the heat equation*, Uspekhi Mat. Nauk **53** (1998), no. 4, 176–177. (Russian)
- A. Ya. Dorogovtsev,
*Periodic processes: A survey of results*, Theory Stoch. Process. **2(18)** (1996), no. 3–4, 36–53.
- Anatolii Ya. Dorogovtsev,
*Time-stationary and time-periodic solutions for boundary value problems*, Proceedings of the Donetsk Colloquium on Probability Theory and Mathematical Statistics (1998), 1998, pp. 105–115. MR **2026618**
- A. Ya. Dorogovtsev,
*Periodic in distribution solution for a telegraph equation*, J. Appl. Math. Stochastic Anal. **12** (1999), no. 2, 121–131. MR **1701228**, DOI https://doi.org/10.1155/S1048953399000131
- A. Ya. Dorogovtsev,
*Stability of stationary solutions*, Dokl. Akad. Nauk **369** (1999), no. 3, 309–310 (Russian). MR **1746744**
- A. Ya. Dorogovtsev,
*Solutions, periodic with respect to distribution, of a boundary value problem for the heat equation*, Dokl. Akad. Nauk **372** (2000), no. 6, 733–735 (Russian). MR **1776913**
- A. Ya. Dorogovtsev,
*Periodic in distribution solution for a telegraph equation*, J. Appl. Math. Stochastic Anal. **12** (1999), no. 2, 121–131. MR **1701228**, DOI https://doi.org/10.1155/S1048953399000131
- A. Ya. Dorogovtsev,
*Bounded solutions of abstract equations*, Novi Sad J. Math. **30** (2000), no. 1, 59–67. MR **1835631**
- A. Ya. Dorogovtsev,
*Stationary solutions to boundary problem for the heat equations*, Hiroshima Math. J. **30** (2000), no. 2, 191–203. MR **1777511**
- A. Ya. Dorogovtsev and O. Yu. Trofimchuk,
*On the stability of stationary solutions of a linear integro-differential equation*, J. Appl. Math. Stochastic Anal. **14** (2001), no. 2, 139–150. MR **1838342**, DOI https://doi.org/10.1155/S1048953301000107
- A. Ya. Dorogovtsev,
*Solutions, periodic in distribution, of a boundary value problem for the heat equation*, Fundam. Prikl. Mat. **7** (2001), no. 3, 699–712 (Russian, with English and Russian summaries). MR **1879292**
- A. Ya. Dorogovtsev,
*Solutions, periodic in distribution, of a boundary value problem for a telegraph equation*, Differ. Uravn. **37** (2001), no. 3, 391–396, 431 (Russian, with Russian summary); English transl., Differ. Equ. **37** (2001), no. 3, 418–424. MR **1846535**, DOI https://doi.org/10.1023/A%3A1019202801360
- A. Ya. Dorogovtsev,
*Periodicity in distribution. I. Discrete systems*, Int. J. Math. Math. Sci. **30** (2002), no. 2, 65–127. MR **1901089**, DOI https://doi.org/10.1155/S0161171202011328
- A. Ya. Dorogovtsev,
*On a case of the existence of homogeneous solutions*, Ukraïn. Mat. Zh. **54** (2002), no. 2, 190–194 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. **54** (2002), no. 2, 233–238. MR **1952819**, DOI https://doi.org/10.1023/A%3A1020134512402
- A. Ya. Dorogovtsev,
*On the stability of solutions of a stochastic equation*, Ukraïn. Mat. Zh. **56** (2004), no. 1, 19–30 (Russian, with English and Ukrainian summaries); English transl., Ukrainian Math. J. **56** (2004), no. 1, 22–36. MR **2060500**, DOI https://doi.org/10.1023/B%3AUKMA.0000031701.23961.e9
- A. Ya. Dorogovtsev,
*Mathematical Analysis: A Modern Approach*, Second edition, “Fakt”, Kiev, 2004. (Russian)

References
- A. Ya. Dorogovtsev,
*Statistical analysis of a difference stochastic equation*, Dopovidi Akad. Nauk Ukraïn. RSR **2** (1959), 120–124; English transl. in Selected Transl. Math. Statist. and Prob., vol. 3, Amer. Math. Soc., Providence, R.I., 1962, pp. 315–319. MR **0154364 (27:4313)**
- A. Ya. Dorogovtsev,
*Confidence intervals associated with the evaluation of parameters*, Dopovidi Akad. Nauk Ukraïn. RSR **4** (1959), 353–358; English transl. in Selected Transl. Math. Statist. and Prob., vol. 3, Amer. Math. Soc., Providence, R.I., 1962, pp. 321–325. MR **0154363 (27:4312)**
- A. Ya. Dorogovtsev,
*Remarks on random processes generated by differential equations*, Dopovidi Akad. Nauk Ukraïn. RSR **7** (1962), 850–852. (Russian) MR **0143250** (26 #809)
- A. Ya. Dorogovtsev,
*Some remarks on the extrapolation of processes generated by differential equations*, Dopovidi Akad. Nauk Ukraïn. RSR **8** (1962), 1006–1010. (Russian) MR **0143005** (26 #572)
- A. Ya. Dorogovtsev,
*Some remarks on differential equations perturbed by periodic random processes*, Ukrain. Mat. Zh. **XIV** (1962), 119–128; English transl. in Selected Transl. Math. Statist. and Prob., vol. 5, Amer. Math. Soc., Providence, R.I., 1965. MR **0141850** (25 #5247)
- A. Ya. Dorogovtsev,
*Correlation functions of vector processes satisfying a certain differential equation*, Ukrain. Mat. Zh. **XIV** (1962), 322–324. (Russian) MR **0155351** (27 #5285)
- A. Ya. Dorogovtsev,
*Statistical Problems for a Class of Non-Stationary Random Processes*, Candidate dissertation, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1962. (Russian)
- A. Ya. Dorogovtsev,
*Some remarks on the processes generated by some differential processes*, Vestnik Kiev University, Ser. Mat. Mekh. **5** (1963), 124–146. (Russian)
- A. Ya. Dorogovtsev,
*Problems of linear extrapolation for a class of vector processes*, Ukrain. Mat. Zh. **XVI** (1964), 830–834. (Russian) MR **0172330** (30 #2549)
- I. I. Gikhman and A. Ya. Dorogovtsev,
*On the stability of solutions of stochastic differential equations*, Ukrain. Mat. Zh. **XVII** (1965), no. 6, 3–21; English transl. in Fifteen Papers on Analysis, vol. 7, Amer. Math. Soc., Providence, R.I., 1968. MR **0281278 (43:6996)**
- A. Ya. Dorogovtsev,
*Certain problems of optimal control of a regression experiment*, Dopovidi Akad. Nauk Ukraïn. RSR Ser. A **12** (1968), 1067–1071; English transl. in Selected Transl. Math. Statist. and Prob., vol. 10, Amer. Math. Soc., Providence, R.I., 1972, pp. 35–41. MR **0247659 (40:922)**
- A. Ya. Dorogovtsev,
*Application of dynamic programming methods to the investigation of a maintenance problem*, Teor. Veroyatnost. i Mat. Statist. **1** (1970), 74–85; English transl. in Theory Probab. Math. Statist. **1** (1974), 73–84. MR **0280176 (43:5897)**
- A. Ya. Dorogovtsev,
*The designing of a regression experiment*, Teor. Veroyatnost. i Mat. Statist. **3** (1970), 56–61; English transl. in Theory Probab. Math. Statist. **3** (1970), 56–61. MR **0283928 (44:1158)**
- A. Ya. Dorogovtsev,
*On a nonparametric estimate of the regression function*, Teor. Veroyatnost. i Mat. Statist. **4** (1971), 62–64; English transl. in Theory Probab. Math. Statist. **4** (1971), 62–64. MR **0288918** (44 #6113)
- V. V. Breĭ, A. Ya. Dorogovtsev, L. V. Pogorelyĭ, and O. A. Makovetskiĭ,
*On the optimal choice of a thinning interval*, Teor. Veroyatnost. i Mat. Statist. **7** (1972), 14–24; English transl. in Theory Probab. Math. Statist. **7** (1972), 11–18. MR **0343356** (49 #8098)
- V. V. Breĭ, A. Ya. Dorogovtsev, and L. V. Pogorelyĭ,
*An evaluation of the characteristics of a certain nonstationary process*, Vychisl. Prikl. Mat. **19** (1973), 137–142. (Russian) MR **0341584** (49 #6332)
- A. Ya. Dorogovtsev and Yu. V. Kartashev,
*On an estimate of the mean value of a stationary process for a given observation time. I*, Teor. Veroyatnost. i Mat. Statist. **8** (1973), 50–58; English transl. in Theory Probab. Math. Statist. **8** (1977), 47–55. MR **0426335** (54 #14279a)
- A. Ya. Dorogovtsev,
*On a certain estimate of an almost periodic signal from an observation in a stationary noise*, Problems of Statistics and Control of Random Processes (A. V. Skorokhod, ed.), Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1973, pp. 74–105. (Russian) MR **0433767** (55 #6739)
- A. Ya. Dorogovtsev,
*Remarks on some properties of a least squares estimate*, Dopovidi Akad. Nauk Ukraïn. RSR Ser. A **7** (1973), 585–590. (Russian) MR **0331679** (48 #10011)
- A. Ya. Dorogovtsev and K. P. Makarenko,
*On least squares estimates of parameters of a certain nonlinear system*, Issled. Operatsiĭ ASU **2** (1973), 42–52. (Russian)
- A. Ya. Dorogovtsev and Yu. V. Kartashev,
*On an estimate of the mean value of a stationary process for a given observation time. II*, Teor. Veroyatnost. i Mat. Statist. **9** (1973), 73–81; English transl. in Theory Probab. Math. Statist. **9** (1977), 77–85. MR **0426336** (54 #14279b)
- A. Ya. Dorogovtsev,
*On the existence and convergence of moments of the least squares estimate in the nonlinear autoregressive model*, Dopovidi Akad. Nauk Ukraïn. RSR Ser. A **12** (1973), 1066–1071. (Russian) MR **0331680** (48 #10012)
- A. Ya. Dorogovtsev,
*On an estimate of the probability of small values of sums of positive random variables*, Teor. Veroyatnost. i Mat. Statist. **9** (1973), 66–72; English transl. in Theory Probab. Math. Statist. **9** (1977), 69–76. MR **0413231** (54 #1348)
- A. Ya. Dorogovtsev,
*On asymptotic properties of least squares estimates for regression coefficients*, Problemy Peredachi Informatsii **IX** (1973), no. 4, 47–57. (Russian) MR **0348949** (50 #1443)
- A. Ya. Dorogovtsev and Yu. V. Kartashev,
*On an estimate of the mean value of a stationary process for a given size of a sample*, Theory Probab. Appl. **XVIII** (1973), no. 4, 871. (Russian)
- A. Ya. Dorogovtsev,
*An estimate of an almost periodic signal constructed from an observation in a stationary noise*, Proceedings of All Union Symposium on Statistics of Random Processes, Kiev, June 5–8, 1973, pp. 68–71. (Russian) MR **0433767** (55 #6739)
- A. Ya. Dorogovtsev,
*The consistency of an estimate of a parameter of a stochastic differential equation*, Teor. Veroyatnost. i Mat. Statist. **10** (1974), 72–81; English transl. in Theory Probab. Math. Statist. **10** (1978), 73–82. MR **0428646** (55 #1667)
- A. Ya. Dorogovtsev and Yu. V. Kartashev,
*Least squares estimation of the regression coefficient for a random process with given observation time*, Teor. Veroyatnost. i Mat. Statist. **10** (1974), 82–87; English transl. in Theory Probab. Math. Statist. **10** (1978), 83–88. MR **0423717** (54 #11692)
- A. Ya. Dorogovtsev,
*Asymptotic properties of estimators of the parameters of a signal that is amplitude modulated by a random process*, Dopovidi Akad. Nauk Ukraïn. RSR Ser. A **8** (1974), 680–684. (Russian) MR **0348950** (50 #1444)
- A. Ya. Dorogovtsev,
*On an estimate of the mean value of a stationary process in the case of restricted possibilities of observation*, Dokl. Akad. Nauk SSSR **214** (1974), no. 2, 261–263; English transl. in Soviet Math. Dokl. **15** (1974), no. 1, 103–105. MR **0341784 (49:6530)**
- A. Ya. Dorogovtsev,
*Asymptotic properties of least squares estimates for a non-linear autoregressive model*, Teoriya Sluchainyh Processov **2** (1974), 47–54. (Russian)
- A. Ya. Dorogovtsev,
*A consistent estimate of a discrete signal from an observation with random errors*, Teor. Veroyatnost. i Mat. Statist., **11** (1974), 26–34; English transl. in Theory Probab. Math. Statist. **11** (1978), 23–31. MR **0394996** (52 #15794)
- A. Ya. Dorogovtsev,
*On a property of an estimator of an almost periodic signal*, Teor. Veroyatnost. i Mat. Statist. **11** (1974), 35–38; English transl. in Theory Probab. Math. Statist. **11** (1978), 33–36. MR **0405757** (53 #9549)
- A. Ya. Dorogovtsev,
*The asymptotic behavior of estimates of parameters of a certain non-linear system*, Kibernetika **4** (1974), 72–77. (Russian) MR **0394995** (52 #15793)
- A. Ya. Dorogovtsev,
*A certain estimate of a periodic signal constructed from an observation in a stationary noise*, Vestnik Kiev University, Ser. Mat. Mekh. Ser. A **16** (1974), 10–25. (Russian) MR **0455240** (56 #13479)
- A. Ya. Dorogovtsev,
*On the consistency of an estimate of the regression function*, Teor. Veroyatnost. i Mat. Statist. **12** (1975), 36–43; English transl. in Theory Probab. Math. Statist. **12** (1978), 35–43. MR **0397973** (53 #1828)
- A. Ya. Dorogovtsev,
*Properties of estimates of parameters in a certain linear regression model*, Vestnik Kiev University, Ser. Mat. Mekh. Ser. A **17** (1975), 3–12. (Russian) MR **0433768** (55 #6740)
- A. Ya. Dorogovtsev and T. A. Sheremet’eva,
*The consistency of an estimate of a transition function*, Theory of Random Processes. Questions of Statistics and Control, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1974, pp. 30–39. (Russian) MR **0488576** (58 #8103)
- A. Ya. Dorogovtsev,
*On the limit distribution of an estimator of a regression function*, Teor. Veroyatnost. i Mat. Statist. **13** (1975), 38–46; English transl. in Theory Probab. Math. Statist. **13** (1977), 39–46. MR **0418326** (54 #6367)
- A. Ya. Dorogovtsev and G. P. Grechka,
*The asymptotic properties of the periodogram estimate of the frequency and amplitude of a harmonic oscillation*, Vychisl. Prikl. Mat. **28** (1976), 18–30. (Russian) MR **0451587 (56:9869)**
- A. Ya. Dorogovtsev,
*On an assertion useful in proving the consistency of estimators*, Teor. Veroyatnost. i Mat. Statist. **14** (1976), 34–41; English transl. in Theory Probab. Math. Statist. **14** (1977), 33–39. MR **0415835** (54 #3912)
- A. Ya. Dorogovtsev,
*On the consistency of non-parametric estimators of a regression function*, Teor. Veroyatnost. i Mat. Statist. **15** (1976), 47–53; English transl. in Theory Probab. Math. Statist. **15** (1978), 46–42. MR **0418327** (54 #6368)
- A. Ya. Dorogovtsev,
*Remarks on the properties of a certain non-parametric maximum likelihood estimate*, Mathematics Collection, “Naukova dumka”, Kiev, 1976, pp. 262–268. (Russian) MR **0468076** (57 #7915)
- A. Ya. Dorogovtsev,
*Properties of a non-parametric estimate of a shift parameter of the simplest stochastic differential equation*, Teoriya Sluchainyh Processov **4** (1976), 51–59. (Russian) MR **0423665** (54 #11640)
- A. Ya. Dorogovtsev and P. S. Knopov,
*Properties of an estimator of parameters of a non-stationary Gaussian regression of a random field*, Teor. Veroyatnost. i Mat. Statist. **15** (1976), 54–68; English transl. in Theory Probab. Math. Statist. **15** (1978), 53–66. MR **0431564** (55 #4561)
- A. Ya. Dorogovtsev and G. P. Grechka,
*Properties of a periodogram estimate of the frequency*, Vestnik Kiev University, Ser. Mat. Mekh. Ser. A **18** (1976), 120–122. (Russian) MR **0494764** (58 #13574)
- A. Ya. Dorogovtsev and P. S. Knopov,
*The consistency of estimates of a continuous function constructed from observations at a finite number of points and with random errors*, Dopovidi Akad. Nauk Ukraïn. RSR Ser. A **12** (1976), 1065–1068. (Russian) MR **0433681** (55 #6653)
- A. Ya. Dorogovtsev and P. S. Knopov,
*An estimator of a two-dimensional signal from an observation with additive random noise*, Teor. Veroyatnost. i Mat. Statist. **17** (1977), 61–79; English transl. in Theory Probab. Math. Statist. **17** (1980), 67–86. MR **0468077** (57 #7916)
- A. Ya. Dorogovtsev and P. S. Knopov,
*Asymptotic properties of a non-parametric estimate of a function of two arguments*, Teoriya Sluchainyh Processov **5** (1977), 27–35. (Russian) MR **0468016** (57 #7857)
- A. Ya. Dorogovtsev,
*Properties of estimates of parameters of linear Gaussian regression in the discrete case*, Vychisl. Prikl. Mat. **31** (1977), 136–146. (Russian) MR **0501671** (58 #18969)
- A. Ya. Dorogovtsev,
*On the convergence of the extremum-points of convergent sequences of random functionals*, Dopovidi Akad. Nauk Ukraïn. RSR Ser. A **7** (1977), 581–584. (Russian) MR **0494627 (58:13457)**
- A. Ya. Dorogovtsev,
*Studies in the Theory of Estimation of Parameters of Random Processes*, Doctoral dissertation, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1977. (Russian)
- A. Ya. Dorogovtsev and M. I. Yuditskiĭ,
*Models with random errors in variables. Estimation of parameters and design of experiments*, Teor. Veroyatnost. i Mat. Statist. **19** (1978), 51–57; English transl. in Theory Probab. Math. Statist. **19** (1980), 57–63. MR **0518967** (58 #24767)
- A. Ya. Dorogovtsev and P. S. Knopov,
*The weak convergence of a sequence of two-parameter martingales*, Dopovidi Akad. Nauk Ukraïn. RSR Ser. A **8** (1978), 675–679. (Russian) MR **0510436 (80c:60066**
- A. Ya. Dorogovtsev, D. S. Silvestrov, A. V. Skorokhod, and M. I. Yadrenko,
*Probability Theory: Collection of Problems*, “Vyshcha Shkola”, Kiev, 1980; English transl., Amer. Math. Soc., Providence, R.I., 1997. MR **1444579 (98k:60001)**
- A. Ya. Dorogovtsev,
*On a problem of determining an unbiased linear estimator with minimal variance*, Teor. Veroyatnost. i Mat. Statist. **22** (1980), 52–57; English transl. in Theory Probab. Math. Statist. **22** (1981), 57–62.
- N. A. Germanov and A. Ya. Dorogovtsev,
*Estimation of parameters of an autoregressive process with non-identically distributed disturbances*, Dopovidi Akad. Nauk Ukraïn. RSR Ser. A **7** (1980), 14–17. (Russian) MR **0582843** (82a:62140)
- A. Ya. Dorogovtsev and A. G. Kurchenko,
*Application of a certain minimization problem in a Hilbert space to the determination of the best linear estimator*, Teor. Veroyatnost. i Mat. Statist. **23** (1980), 47–51; English transl. in Theory Probab. Math. Statist. **23** (1981), 51–54. MR **0614575 (82m:62144)**
- A. Ya. Dorogovtsev and A. G. Kurchenko,
*The best linear estimator of the trend parameters in the presence of white noise type errors*, Teor. Veroyatnost. i Mat. Statist. **24** (1981), 27–34; English transl. in Theory Probab. Math. Statist. **24** (1982), 31–37. MR **0628425 (83f:62135)**
- A. Ya. Dorogovtsev, A. A. Kurchenko, and A. G. Kukush,
*A new case for the existence of linear unbiased estimates*, Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk **3** (1981), 23–29. (Russian) MR **0628914** (83a:62182)
- A. Ya. Dorogovtsev,
*The Theory of Estimates of the Parameters of Random Processes*, “Vyshcha shkola”, Kiev, 1982. (Russian) MR **0668517 (84h:62122)**
- A. Ya. Dorogovtsev,
*Mathematics Today* (A. Ya. Dorogovtsev, ed.), vol. 1–9, “Vyshcha shkola”, Kiev, 1983–1994; vol. 10–11, “TViMS”, Kiev, 1995–1997; vol. 12, “Nauchno-metodicheskii tsentr vysshego obrazovaniya”, Kiev, 2001. (Russian) MR **1632323 (99h:47016)**
- A. Ya. Dorogovtsev,
*Estimation of the mean value parameter in a Hilbert space*, Teoriya Sluchainyh Processov **11** (1983), 28–31. (Russian) MR **0711232 (85b:62024)**
- A. Ya. Dorogovtsev and Yu. G. Kondrat’ev,
*Some problems of infinite-dimensional analysis and their applications*, Vīsnyk Kyïv. Unīv. Ser. Mat. Mekh. **25** (1983), 55–70. (Russian) MR **0746765 (87a:46072)**
- A. Ya. Dorogovtsev and A. G. Kukush,
*Optimal choice of the observation mode in a problem of estimation of the mean*, Teor. Veroyatnost. i Mat. Statist. **30** (1984), 38–45; English transl. in Theory Probab. Math. Statist. **30** (1985), 39–46. MR **0800828 (87d:62163)**
- A. Ya. Dorogovtsev,
*The convergence of some integrals with respect to the Gaussian measure in a Hilbert space*, Dopovidi Akad. Nauk Ukraïn. RSR Ser. A **5** (1985), 7–8. (Russian) MR **0796167 (86j:60009)**
- A. Ya. Dorogovtsev, S. D. Ivasishen, and A. G. Kukush,
*Asymptotic behavior of solutions of the heat equation with white noise in the right-hand side*, Ukrain. Mat. Zh. **37** (1985), no 1, 13–20; English transl. in Ukrainian Math. J. **37** (1986), 10–15. MR **0780908 (86m:35016)**
- A. Ya. Dorogovtsev,
*The asymptotic behavior of solutions of the Cauchy problem for an abstract stochastic differential equation*, Uspekhi Mat. Nauk **41** (1986), no. 4, 159–160. (Russian)
- A. Ya. Dorogovtsev,
*Asymptotic properties of estimates of nonlinear regression in Hilbert space*, Teor. Veroyatnost. i Mat. Statist. **35** (1986), 36–43; English transl. in Theory Probab. Math. Statist. **35** (1987), 37–44. MR **0885663 (88d:62058)**
- A. Ya. Dorogovtsev,
*Mathematical Analysis*, A collection of problems, “Vyshcha Shkola”, Kiev, 1987. (Russian)
- A. Ya. Dorogovtsev, N. Zerek, and A. G. Kukush,
*Weak convergence to the normal distribution of an estimator of an infinite-dimensional parameter*, Teor. Veroyatnost. i Mat. Statist. **37** (1987), 39–46; English transl. in Theory Probab. Math. Statist. **37** (1988), 45–51. MR **0913908 (89h:62095)**
- N. A. Denis’evskiĭ and A. Ya. Dorogovtsev,
*On a law of large numbers for a linear process in a Banach space*, Dokl. Akad. Nauk SSSR **295** (1987), no. 2, 276–279; English transl. in Soviet Math. Dokl. **36** (1988), no. 1, 47–50. MR **0902681 (88j:60023)**
- A. Ya. Dorogovtsev,
*The existence of periodic solutions of an abstract stochastic equation. The asymptotic periodicity of solutions of the Cauchy problem*, Uspekhi Mat. Nauk **42** (1987), no. 4, 160. (Russian)
- A. Ya. Dorogovtsev, S. D. Ivasishen, and A. G. Kukush,
*On the asymptotic behavior on the linear stochastic heat equation solutions*, Probability Theory and Mathematical Statistics, Proceedings of the Fourth Vilnius Conference, vol. 1, VNU Sci. Press, Utrecht, 1987, pp. 419–432. MR **0901501 (89g:60192)**
- A. Ya. Dorogovtsev and A. G. Kukush,
*Asymptotic behavior of the solution of the Cauchy problem for a stochastic equation of parabolic type*, Ukrain. Mat. Zh. **40** (1988), no. 2, 162–169; English transl. in Ukrainian Math. J. **40** (1988), no. 2, 136–142. MR **0941500 (89e:60117)**
- A. Ya. Dorogovtsev and A. G. Kukush,
*On the limiting distribution of extremum points for certain stochastic optimization models*, Lecture Notes in Control and Inform. Sci., vol. 81, Springer-Verlag, Berlin, 1986, 17–21. MR **0890965 (88g:93116)**
- A. Ya. Dorogovtsev,
*Asymptotic behavior of solutions of the Cauchy problem for an abstract stochastic differential equation*, Teor. Veroyatnost. i Mat. Statist. **38** (1988), 31–34; English transl. in Theory Probab. Math. Statist. **38** (1989), 31–34. MR **0947518 (89g:60183)**
- A. Ya. Dorogovtsev,
*The existence of periodic solutions of an abstract stochastic equation. Asymptotic periodicity of solutions of the Cauchy problem*, Teor. Veroyatnost. i Mat. Statist. **39** (1988), 47–52; English transl. in Theory Probab. Math. Statist. **39** (1989), 55–60. MR **0947930 (89e:60119)**
- A. Ya. Dorogovtsev and Le Vin’Tkhuan,
*The existence of periodic and stationary regimes of discrete dynamical systems in a Banach space*, Kibernetika **6** (1988), 121–123. (Russian) MR **0986181 (90f:60114)**
- A. Ya. Dorogovtsev and O. Ortega,
*The existence of periodic solutions of a stochastic equation in a Hilbert space*, Vīsnyk Kyïv. Unīv. Ser. Mat. Mekh. **30** (1988), 21–30. (Russian) MR **004452 (90k:60107)**
- A. Ya. Dorogovtsev and Le Vin’Tkhuan,
*Correlation functions of Gaussian Markov stationary and periodic processes in a Hilbert space*, Selected Problems in the Current Theory of Random Processes, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1988, pp. 61–65. (Russian)
- M. F. Gorodniĭ and A. Ya. Dorogovtsev,
*Stationary solutions of a two-dimensional stochastic difference equation in a Banach space*, Stochastic Analysis and its Applications, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1989, pp. 25–33. (Russian) MR **1064769 (91i:60167)**
- A. Ya. Dorogovtsev,
*Elements of the General Theory of Measure and Integral*, “Vyshcha shkola”, Kiev, 1989. (Russian) MR **0995843 (90f:28001)**
- A. Ya. Dorogovtsev,
*Periodic solutions of evolution differential equations that are perturbed by stochastic processes*, Ukrain. Mat. Zh. **41** (1989), no. 12, 1642–1648; English transl. in Ukrainian Math. J. **41** (1990), no. 12, 1412–1419. MR **1042961 (91i:34068)**
- A. Ya. Dorogovtsev,
*Necessary and sufficient conditions for existence of stationary and periodic solutions of a stochastic difference equation in Hilbert space*, Comput. Math. Appl. **19** (1990), no. 1, 31–37. MR **1026779 (91d:60149)**
- A. Ya. Dorogovtsev,
*Stationary and periodic solutions of a stochastic difference equation in a Banach space*, Teor. Veroyatnost. i Mat. Statist. **42** (1990), 35–42; English transl. in Theory Probab. Math. Statist. **42** (1991), 39–46. MR **1069311 (92f:60113)**
- A. Ya. Dorogovtsev,
*Stochastically periodic solutions of differential equations with operator coefficients*, Ukrain. Mat. Zh. **43** (1991), no. 4, 489–496; English transl. in Ukrainian Math. J. **43** (1991), no. 4, 451–457. MR **1117890 (92i:60123)**
- A. Ya. Dorogovtsev,
*Consistency of the least squares estimator of an infinite-dimensional parameter*, Sibirsk. Mat. Zh. **33** (1992), no. 4, 65–69; English transl. in Siberian Math. J. **33** (1993), no. 4, 603–607. MR **1185436 (93h:62119)**
- A. Ya. Dorogovtsev,
*Periodic and Stationary Regimes of Infinite-Dimensional Deterministic and Stochastic Dynamical Systems*, “Vyshcha Shkola”, Kiev, 1992. (Russian) MR **1206004 (94c:60097)**
- A. Ya. Dorogovtsev,
*Bounded and periodic solutions of some difference and differential equations*, Uspekhi Mat. Nauk **46** (1991), no. 6, 149–150. (Russian)
- A. Ya. Dorogovtsev,
*Mathematical Analysis*, vol. I, “Lybid”, Kyiv, 1993; vol. II, 1994. (Russian)
- A. Ya. Dorogovtsev,
*On asymptotic normality of the least square estimators of an infinite-dimensional parameter*, Ukrain. Mat. Zh. **45** (1993), no. 1, 44–53; English transl. in Ukrainian Math. J. **45** (1993), no. 1, 48–58. MR **1426569 (99c:62058)**
- A. Ya. Dorogovtsev,
*Periodic and bounded solutions of the operator Riccati equation*, Ukrain. Mat. Zh. **45** (1993), no. 2, 239–242; English transl. in Ukrainian Math. J. **45** (1993), no. 2, 255–259. MR **1232407 (95a:34092)**
- A. Ya. Dorogovtsev,
*Stationary and periodic solutions of the operator Riccati equation with random perturbation*, Ukrain. Mat. Zh. **45** (1993), no. 5, 609–615; English transl. in Ukrainian Math. J. **45** (1994), no. 5, 662–670. MR **1247681 (94k:34107)**
- A. Ya. Dorogovtsev and M. F. Gorodniĭ,
*Bounded solutions of the operator Volterra chain*, Uspekhi Mat. Nauk **49** (1994), no. 4, 85.
- A. Ya. Dorogovtsev,
*Stationary and periodic solutions of linear differential operator equations*, Proceedings of the Second Ukrainian–Hungarian Conference on “New Trends in Probability Theory and Mathematical Statistics”, September 25–October 2, 1992, Mukachevo, Ukraine, TViMS, Kiev, 1994, pp. 50–54.
- A. Ya. Dorogovtsev and T. A. Petrova,
*Bound and periodic solutions of the Riccati equation in Banach space*, J. Appl. Math. Stochastic Anal. **8** (1995), no. 2, 195–200. MR **1330123 (96c:34129)**
- M. F. Gorodniĭ and A. Ya. Dorogovtsev,
*Bounded solutions of a class of nonlinear operator difference equations*, Ukrain. Mat. Zh. **47** (1995), no. 7, 888–894; English transl. in Ukrainian Math. J. **47** (1995), no. 7, 890–896. MR **1367944 (96j:39016)**
- A. Ya. Dorogovtsev,
*Stability of periodic solutions of operator equations with perturbation coefficients*, Exploring the Stochastic Laws, VSP, 1995, pp. 111–119. MR **1713997 (2001g:60163)**
- A. Ya. Dorogovtsev,
*Stationary and periodic solutions of a certain class of nonlinear equations in a Banach space*, Theory Stoch. Process. **1(17)** (1995), no. 1, 17–25.
- A. Ya. Dorogovtsev and T. A. Petrova,
*Bounded and periodic solutions of a Riccati type equation in a Banach space*, Dopovidi NAN Ukraïny **9** (1995), 8–9. (Russian) MR **1374671 (96j:34108)**
- A. Ya. Dorogovtsev,
*Bounded and periodic solutions of the operator Riccati equation with an unbounded operator*, Dopovidi NAN Ukraïny **10** (1995), 7–9. (Russian) MR **1376464**
- A. Ya. Dorogovtsev,
*On the stability of bounded and stationary solutions of equations with operator coefficients in the case where the coefficients are disturbed*, Uspekhi Mat. Nauk **50** (1995), no. 4, 103. (Russian)
- A. Ya. Dorogovtsev,
*Asymptotic properties of an estimator of the compensator of a nonhomogeneous Poisson process*, Proceedings of the International Mathematical Conference dedicated to the memory of Hans Hahn, October 1994, Chernivtsi, “Ruta”, Chernivtsi, 1995, pp. 72–77. (Russian)
- A. Ya. Dorogovtsev and A. G. Kukush,
*Asymptotic properties of a nonparametric estimator of the intensity of a nonhomogeneous Poisson process*, Kibernet. Sistem. Anal. **1** (1996), 91–104; English transl. in Cybernet. Systems Anal. **32** (1996), no. 1, 74–85. MR **1409534 (97k:62077)**
- A. Ya. Dorogovtsev,
*The stability of bounded and stationary solutions of linear equations in the case of disturbed operator coefficients*, Dokl. Akad. Nauk **345** (1995), no. 4, 488–450. (Russian) MR **1376444 (96k:47123)**
- A. Ya. Dorogovtsev and T. A. Petrova,
*Bounded and periodic solutions of the Riccati operator equation with an unbounded operator*, Differ. Uravn. **33** (1997), no. 3, 309–315; English transl. in Differential Equations **33** (1997), no. 3, 305–311. MR **1615401 (98k:34101)**
- A. Ya. Dorogovtsev,
*Stability of stationary and periodic solutions equations in Banach space*, J. Appl. Math. Stochastic Anal. **10** (1977), no. 3, 249–255. MR **1468119 (99a:60063)**
- A. Ya. Dorogovtsev,
*Stationary solutions of semilinear abstract equation with random input*, Nonlinear Stud. **5** (1998), no. 2, 129–138. MR **1652614 (99h:34083)**
- A. Ya. Dorogovtsev,
*Solutions, periodic in distribution, of the boundary value problem for the heat equation*, Uspekhi Mat. Nauk **53** (1998), no. 4, 176–177. (Russian)
- A. Ya. Dorogovtsev,
*Periodic processes: A survey of results*, Theory Stoch. Process. **2(18)** (1996), no. 3–4, 36–53.
- A. Ya. Dorogovtsev,
*Time-stationary and time-periodic solutions for boundary value problems*, Theory Stoch. Process. **4(20)** (1998), no. 1–2, 105–115. MR **2026618 (2005f:60137)**
- A. Ya. Dorogovtsev,
*Periodic in distribution solution for a telegraph equation*, J. Appl. Math. Stochastic Anal. **12** (1999), no. 2, 121–131. MR **1701228 (2001i:35311)**
- A. Ya. Dorogovtsev,
*Stability of stationary solutions*, Dokl. Akad. Nauk **369** (1999), no. 3, 309–310. (Russian) MR **1746744 (2001g:60161)**
- A. Ya. Dorogovtsev,
*Solutions, periodic with respect to distribution, of a boundary value problem for the heat equation*, Dokl. Akad. Nauk **372** (2000), no. 6, 733–735. (Russian) MR **1776913**
- A. Ya. Dorogovtsev,
*Periodic in distribution solution for a telegraph equation*, J. Appl. Math. Stochastic Anal. **12** (1999), no. 2, 121–131. MR **1701228 (2001i:35311)**
- A. Ya. Dorogovtsev,
*Bounded solutions of abstract equations*, Novi Sad J. Math. **30** (2000), no. 1, 59–67. MR **1835631 (2002e:34092)**
- A. Ya. Dorogovtsev,
*Stationary solutions to boundary problem for the heat equations*, Hiroshima Math. J. **30** (2000), no. 2, 191–203. MR **1777511 (2001i:35310)**
- A. Ya. Dorogovtsev and O. Yu. Trofimchuk,
*On the stability of stationary solutions of a linear integro-differential equation*, J. Appl. Math. Stochastic Anal. **14** (2001), no. 2, 139–150. MR **1838342 (2002f:45018)**
- A. Ya. Dorogovtsev,
*Solutions, periodic in distribution, of a boundary value problem for the heat equation*, Fundam. Prikl. Mat. **7** (2001), no. 3, 699–712. (Russian) MR **1879292 (2002j:35329)**
- A. Ya. Dorogovtsev,
*Solutions, periodic in distribution, of a boundary value problem for a telegraph equation*, Differ. Uravn. **37** (2001), no. 3, 391–396, 431; English transl. in Differ. Equ. **37** (2001), no. 3, 418–424. MR **1846535 (2002c:35024)**
- A. Ya. Dorogovtsev,
*Periodicity in distribution. I. Discrete systems*, Int. J. Math. Math. Sci. **30** (2002), no. 2, 65–127. MR **1901089 (2003f:47058)**
- A. Ya. Dorogovtsev,
*On a case of the existence of homogeneous solutions*, Ukrain. Mat. Zh. **54** (2002), no. 2, 190–194; English transl. in Ukrainian Math. J. **54** (2002), no. 2, 233–238. MR **1952819 (2003k:60168)**
- A. Ya. Dorogovtsev,
*On the stability of solutions of a stochastic equation*, Ukrain. Mat. Zh. **56** (2004), no. 1, 19–30; English transl. in Ukrainian Math. J. **56** (2004), no. 1, 22–36. MR **2060500 (2005a:60091)**
- A. Ya. Dorogovtsev,
*Mathematical Analysis: A Modern Approach*, Second edition, “Fakt”, Kiev, 2004. (Russian)

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Published electronically:
January 4, 2006

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American Mathematical Society